Divisibility · Beginner

Divisibility by 3

Add the digits; the integer is divisible by 3 when its digit sum is.

01

The fast method

1 + 2 + 3 = 6, which is divisible by 3.

How it works

Add the digits; the integer is divisible by 3 when its digit sum is. Every power of 10 has remainder 1 when divided by 3.

02

Why it works

Every power of 10 has remainder 1 when divided by 3.
Use it when

Applies to integers written in base ten; use absolute value for negative integers.

Watch out for

The rule checks divisibility; it does not calculate the quotient.

03

Verified examples

Example 1

Is 123 divisible by 3?

1 + 2 + 3 = 6, which is divisible by 3.

Yes
Example 2

Is 452 divisible by 3?

4 + 5 + 2 = 11, which is not divisible by 3.

No
Example 3

Is 780 divisible by 3?

7 + 8 + 0 = 15, which is divisible by 3.

Yes